Step 1) You will need to go to the website Nexus mods https://www.nexusmods.com/ and make an account if you haven't already (don't worry it's safe for the most part). Then use the Nexus search bar to look for Batman: Arkham Knight, and download the mod you want. To make this quicker I'll link the MAN suit mod page as well.
https://www.nexusmods.com/batmanarkhamknight/mods/881

Step 2) This goes without saying, but make sure you have Batman: Arkham Knight installed with all its DLC. Why do you need all its DLC? Well, in this case you would only really need the 1989 suit and Batmobile installed, but a lot of the mods for this game rely on the DLC. So it's better in the long run to have all the DLC on your hard drive to avoid the game crashing.

Step 3) Once the Mod is finished downloading extract the file from your downloads folder using a extraction tool of your choice. Examples would be 7-zip, Winrar or hell even just the built in Windows extraction tools, as I've found they work just fine.

Step 4) In your Steam library look for Arkham Knight and click on it's profile, you should see a setting icon, click it, then click manage, and go to browse local files.

Step 5) Once there click the folder called DLC, you will be greeted by a lot of numbered folders. I've fond that the folder 418930 works the best for modding but It should work with any of the numbered folders. Place the extracted file from Nexus into the folder and press the big green play button in Steam.